Final answer:
The subject deals with the determination of optimal strategies and the value of the game in game theory, specifically in strategic games such as the ultimatum game and the prisoner's dilemma. The analysis of expected earnings and average winnings, as well as the house advantage, play significant roles in defining the best course of actions for players.
Step-by-step explanation:
The querent appears to be asking about how to determine optimal strategies and the value of the game within the context of game theory. In many strategic games, such as the ultimatum game or the prisoner's dilemma, players are confronted with decisions that require them to predict the actions of others to maximize their own outcomes. The optimal strategy typically balances the potential gains with the risks involved, taking into account the incentives and likely responses of the other players.
In the ultimatum game, a rational player A would tend to offer the smallest amount possible, anticipating that player B would accept any amount that is better than nothing. However, human psychology and notions of fairness can influence player B to reject offers perceived as too low, despite the cost to themselves. This illustrates a divergence from purely rational behavior.
When analyzing the prisoner's dilemma, the players' decision to cooperate or defect is analyzed. If players can communicate, they might be able to overcome the dilemma by reaching an agreement that ensures a better outcome for both, albeit against their individual incentives to defect.
In terms of expected earnings and average winnings, one must consider the probabilities of various outcomes and calculate the expected value. The player will then compare these expected values to decide whether to accept a deal. In the context of the house advantage, it is necessary to quantify this over a large number of games to determine the long-term prospects of players versus the house. If expected losses are higher than expected gains, the house has the advantage.